Amateur Draft
 

In OOTP19, the amateur draft provided enough players for up 72 rounds (if not more players), however, my second draft since moving over to OOTP20 has again provided fewer players than 5 rounds (only 156 eligible players). I have checked several settings and see no way to rectify this. Is this another programming glitch or is there a setting that I can change so that I have a suitable number of players?

Tough to say for sure without knowing what settings you have checked, but here is something to look at in case you have not.

The settings in the screenshot below can be found under the RULES tab in your League Settings page. Circled one will determine how many rounds of available players there will be. This will work with both fictional and historical databases with one exception. If the available pool is set for 5, it will not matter how long your draft is... you will only have 5 rounds of players available.

The exception:
If you are playing historical, but not random debut... you will only have as many available players as debuted that season. This happens often pre 1950 where you may only get 3 to 5 rounds worth of players assuming you are using the default number of teams for that season. If you double the number of teams via expansion, you will only have enough players for half the number of rounds.

Looked for it
 

I do not have the options "import players for X rounds" available. I do have the number of rounds to select, but the next line is not there.

It sounds like you are playing historical mode without random debut set. Need some more information to make an educated guess and help you out.

What mode did you use to create the league you are playing? Fictional, Quick Start, or Historical? (I am guessing Historical). What season is your league currently in?

If Historical, and you did not make other changes, then Random Debut is not on and that is the reason for the limit.

I cant open the game at the moment, but if you look through your settings you should see a checkbox for random debut.

Checkbox in attached screenshot.

You are correct
 

I started the game with the 1985 Toronto Blue Jays and am now in the 2013 season. While playing the game in the OOTP19 game, I could have up to 72 rounds in the draft and enough players for the entire draft. The "Use random rookies from all eras" was not ticked. The same exists for the version of OOTP20, that box is also not ticked, but when I transferred the game to OOTP20, the draft pool shrank tremendously, i.e., my 2013 draft only had 156 players available for 40 rounds.

Playing with the default database, you will should not get that many available players for the draft unless import & maintain real minor leagues is checked. The downside of this is having your minor league team names and setup changed by the game, but it will give you the draft numbers you are expecting. That setting must not have carried over with your import for some reason.

For example, running 1985 Jays with a 26 team league, I had enough players for a little over 5 rounds. With the Import minors setting checked I had enough amateurs for 43 rounds.

This setting is initially set in the game creation screen on the first panel of the wizard under the selection for Import Complete History. If you go ahead and change it in your current game via the setting in the screenshot below you should see the larger number of players you are accustomed to the next time a pool is generated.

I believe the check block to “import players for x rounds” shows up only during spring training, or that is when I have set it in the past.